MySQL TIMESTAMP to default NULL, not CURRENT_TIMESTAMP

Using MySQL, I'm trying to make a timestamp column from a date column and a time column. If the date or time column contains a NULL value, MySQL automatically sets the corresponding value in the TIMESTAMP column to the CURRENT_TIMESTAMP.

Is there a way to make it default to a NULL, instead of the CURRENT_TIMESTAMP?

Something like:

ALTER TABLE customers ADD s_timestamp TIMESTAMP;
UPDATE customers
    SET s_timestamp = timestamp(s_date,s_time) DEFAULT NULL;